Anti-reflection coatings are formed by a physical vapor deposition method such as vacuum vapor deposition, sputtering, ion plating, etc., or a liquid-phase method such as a sol-gel method. The anti-reflection coatings should have smaller refractive indices than those of substrates, but even the smallest-refractive-index MgF2 obtained by a physical vapor deposition method has as relatively large a refractive index as 1.38. This refractive index is larger than an ideal level (1.2-1.25) of anti-reflection coatings for glass or plastic lenses (refractive index: about 1.5-1.9). An anti-reflection coating having a refractive index of 1.2-1.25 exhibits reflectance of less than 1% in a visible-light region having a wavelength of 400-700 nm, while an anti-reflection coating made of MgF2 having a refractive index of 1.38 has reflectance of more than 1%.
Silica aerogel obtained by the sol-gel method has a smaller refractive index than that of MgF2. U.S. Pat. No. 5,948,482 discloses a method for producing aerogel usable for anti-reflection coatings, comprising the steps of preparing a colloidal sol, turning it to gel by aging, modifying a gel surface with a non-aqueous, organic group in a non-aqueous medium, turning the surface-modified gel to sol by a ultrasonic treatment in a non-aqueous medium, and applying the sol to a substrate. The resultant aerogel coating has porosity of up to 99% (low refractive index), but it is poor in scratch resistance.
“Journal of Sol-Gel Science and Technology,” 2000, Vol. 18, pp. 219-224 proposes a method for producing a nanoporous silica coating having excellent scratch resistance comprising the steps of hydrolyzing and polymerizing tetraethoxysilane in the presence of ammonia in a mixed solvent of ethanol and water at 80° C. for 2-20 hours to prepare an alkaline sol, adding tetraethoxysilane, water and hydrochloric acid and aging the resultant mixture at 60° C. for 15 days, applying the formed sol to a substrate, drying it at 80° C. for 30 minutes, and heat-treating it in a mixed gas of ammonia and steam or in the atmosphere at 400° C. for 30 minutes. However, this method needs 15-day aging, meaning low efficiency, and the resultant nanoporous silica coating does not have sufficient scratch resistance.